Mário José de Oliveira

University of São Paulo | USP · Institute of Physics University of São Paulo

We propose an expression for the production of entropy for a system described by a stochastic dynamics which is appropriate for the case where the reverse transition rate vanishes but the forward transition is nonzero. The expression is positive definite and based on the inequality x ln ⁡ x − ( x − 1 ) ⩾ 0 . The corresponding entropy flux is linear...

A teoria de Carnot é singular entre as teorias do calor desenvolvidas antes do surgimento da termodinâmica por considerar a relação entre calor e trabalho. A teoria está contida no livro de Carnot publicado em 1824, que contém as ideias básicas do funcionamento das máquinas térmicas entre elas a necessidade de uma diferença de temperaturas. O princ...

We investigate the thermodynamics as well as the population dynamics of ecosystems based on a stochastic approach in which the number of individuals of the several species of the ecosystem are treated as stochastic variables. The several species are connected by feeding relationships that are understood as unidirectional processes in which a certai...

We derive the equations of quantum mechanics and quantum thermodynamics from the assumption that a quantum system can be described by an underlying classical system of particles. Each component φ j of the wave vector is understood as a stochastic complex variable whose real and imaginary parts are proportional to the coordinate and momentum associa...

From classical stochastic equations of motion, we derive the quantum Schrödinger equation. The derivation is carried out by assuming that the real and imaginary parts of the wave function \(\phi\) are proportional to the coordinates and momenta associated with the degrees of freedom of an underlying classical system. The wave function \(\phi\) is a...

The majority vote model is one of the simplest opinion systems yielding distinct phase transitions and has garnered significant interest in recent years. This model, as well as many other stochastic lattice models, are formulated in terms of stochastic rules with no connection to thermodynamics, precluding the achievement of quantities such as powe...

We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert space of dimension $n$ which is obtained by a peculiar canonical transformation that changes a pair of real ca...

From classical stochastic equations of motion we derive the quantum Schr\"odinger equation. The derivation is carried out by assuming that the real and imaginary parts of the wave function $\phi$ are proportional to the coordinates and momenta associated to the degrees of freedom of an underlying classical system. The wave function $\phi$ is assume...

We show that the quantum Fokker-Planck equation, obtained by a canonical quantization of its classical version, can be transformed into an equation of the Lindblad form. This result allows us to conclude that the quantum Fokker-Planck equation preserves the trace and positivity of the density operator. The Fokker-Planck structure gives explicit exp...

An interesting concept that has been underexplored in the context of time-dependent simulations is the correlation of total magnetization, $C(t)$%. One of its main advantages over directly studying magnetization is that we do not need to meticulously prepare initial magnetizations. This is because the evolutions are computed from initial states wit...

We show that models of opinion formation and dissemination in a community of individuals can be framed within stochastic thermodynamics from which we can build a nonequilibrium thermodynamics of opinion dynamics. This is accomplished by decomposing the original transition rate that defines an opinion model into two or more transition rates, each re...

The majority vote model is one of the simplest opinion systems yielding distinct phase transitions and has garnered significant interest in recent years. However, its original formulation is not, in general, thermodynamically consistent, precluding the achievement of quantities such as power and heat, as well as their behaviors at phase transition...

The chiral Potts model is studied by means of the real space renormalization group. We use the renormalization group scheme proposed by Niemeyer and Van Leeuwen with an approximation that retains only the first term in the cumulant expansion. The recurrence relations are obtained for any number of states, renormalization factor and lattice dimensio...

We show that the quantum Fokker-Planck equation, obtained by a canonical quantization of its classical version, can be transformed into an equation of the Lindblad form. This result allows us to conclude that the quantum Fokker-Planck equation preserves the trace and positivity of the density operator. The Fokker-Planck structure gives explicit exp...

We use a canonical quantization procedure to obtain the quantum Fokker–Planck equation for a system of interacting particles, which can be either bosons or fermions. Based on this equation, we develop a quantum stochastic thermodynamics of equilibrium and nonequilibrium systems. The approach is applied to a system in contact with two reservoirs of...

We analyze a stochastic approach to population dynamics in which the number of individuals in each class is treated as a stochastic variable. The description of the dynamics is based on the Fokker-Planck equation from which we show that the time evolution of the average number of individuals are identified as the differential equations of the deter...

We show that models of opinion formation and dissemination in a community of individuals can be framed within stochastic thermodynamics from which we can build a nonequilibrium thermodynamics of opinion dynamics. This is accomplished by decomposing the original transition rate that defines an opinion model into two or more transition rates, each re...

We study closed systems of particles that are subject to stochastic forces in addition to the conservative forces. The stochastic equations of motion are set up in such a way that the energy is strictly conserved at all times. To ensure this conservation law, the evolution equation for the probability density is derived using an appropriate interpr...

We study closed systems of particles that are subject to stochastic forces in addition to the conservative forces. The stochastic equations of motion are set up in such a way that the energy is strictly conserved at all times. To ensure this conservation law, the evolution equation for the probability density is derived using an appropriate interpr...

We analyze the susceptible-infected-susceptible model for epidemic spreading in which a fraction of the individuals become immune by vaccination. This process is understood as a dilution by vaccination, which decreases the fraction of the susceptible individuals. For a nonzero fraction of vaccinated individuals, the model predicts a new state in wh...

We examine the development of the concept of parametric invariance in classical mechanics, quantum mechanics, statistical mechanics, and thermodynamics, and particularly its relation to entropy. The parametric invariance was used by Ehrenfest as a principle related to the quantization rules of the old quantum mechanics. It was also considered by Ra...

We examine the concept of probability from its emergence within the realm of the games of chance and the development of the theory of probability until the appearance of the treatise of Kolmogorov on this subject. The discipline related to that theory is framed as the science of aleatory events. Probability is understood as a primitive concept repr...

We examine the analytical theories of heat developed by Laplace, Poisson and Carnot, and the thermodynamic theories based on the energy conservation and the principle of the increase of entropy formulated by Clausius. We present an analysis of the approaches developed by Maxwell, Gibbs, Planck, Duhem, Nernst, and De Donder as well as the irreversib...

We examine the development of the concept of parametric invariance in classical mechanics, quantum mechanics, statistical mechanics, and thermodynamics, and particularly its relation to entropy. The parametric invariance was used by Ehrenfest as a principle related to the quantization rules of the old quantum mechanics. It was also considered by Ra...

We analyze the susceptible-infected-susceptible model for epidemic spreading in which a fraction of the individuals become immune by vaccination. This process is understood as a dilution by vaccination, which decreases the fraction of the susceptible individuals. For a nonzero fraction of vaccinated individuals, the model predicts a new state in wh...

We analyze the effect of immunization by vaccination on deterministic models for epidemic spreading. We use an approach to vaccination in which the number of individuals that acquire immunization by vaccination is considered to be a given function of time. For the susceptible–infected–susceptible model, if the fraction of individuals that in the lo...

We present an analysis of the first analytical physical theories developed after the introduction of calculus. The underlying framework of these theories is the differential and integral calculus in the form developed by Leibniz. We point out the fundamental laws, or principles, or postulates upon which they are founded, and show some results or la...

A scientific theory consists of a symbolic framework containing laws and concepts that are derived by deductive reasoning from fundamental laws and primitive concepts, and complemented by the correspondence or the relation between the symbolic concepts and the real objects. The symbolic framework is understood as a representation of the real, const...

We present an analysis of six deterministic models for epidemic spreading. The evolution of the number of individuals of each class is given by ordinary differential equations of the first order in time, which are set up by using the laws of mass action providing the rates of the several processes that define each model. The epidemic spreading is c...

We analyze four models of epidemic spreading using a stochastic approach in which the primary stochastic variables are the numbers of individuals in each class. The stochastic approach is described by a master equation and the transition rates for each process such as infection or recovery are set up by using the law of mass action. We perform nume...

We analyze a molecular model to describe the phase transitions between the isotropic, nematic, smectic-A, and smectic-C phases. The smectic phases are described by the use of a pair potential, which lacks the full rotational symmetry because of the cylindrical symmetry around the smectic axis. The tilt of the long molecules inside the smectic layer...

We analyze the stochastic thermodynamics of systems with a continuous space of states. The evolution equation, the rate of entropy production, and other results are obtained by a continuous time limit of a discrete time formulation. We point out the role of time reversal and of the dissipation part of the probability current on the production of en...

We analyze four models of epidemic spreading using a stochastic approach in which the primary stochastic variables are the numbers of individuals in each class. The stochastic approach is described by a master equation and the transition rate for each process such as infection or recovery are set up by using the law of mass action. We perform numer...

The stochastic thermodynamics provides a framework for the description of systems that are out of thermodynamic equilibrium. It is based on the assumption that the elementary constituents are acted by random forces that generate a stochastic dynamics, which is here represented by a Fokker-Planck-Kramers equation. We emphasize the role of the irreve...

We analyze the stochastic thermodynamics of systems with continuous space of states. The evolution equation, the rate of entropy production, and other results are obtained by a continuous time limit of a discrete time formulation. We point out the role of time reversal and of the dissipation part of the probability current on the production of entr...

The stochastic thermodynamics provides a framework for the description of systems that are out of thermodynamic equilibrium. It is based on the assumption that the elementary constituents are acted by random forces that generate a stochastic dynamics, which is here represented by a Fokker-Planck-Kramers equation. We emphasize the role of the irreve...

The positivity of the heat capacity is the hallmark of thermal stability of systems in thermodynamic equilibrium. We show that this property remains valid for systems with negative derivative of energy with respect to temperature, as happens to some system described by the microcanonical ensemble. The demonstration rests on considering a trajectory...

Using stochastic thermodynamics, the properties of interacting linear chains subject to periodic drivings are investigated. The systems are described by Fokker-Planck-Kramers equation and exact solutions are obtained as functions of the modulation frequency and strength constants. Analysis will be carried out for short and long chains. In the forme...

We study the properties of nonequilibrium systems modelled as spin models without defined Hamiltonian as the majority voter model. This model has transition probabilities that do not satisfy the condition of detailed balance. The lack of detailed balance leads to entropy production phenomena, which are a hallmark of the irreversibility. By consider...

We give an account and a critical analysis of the use of exact and inexact differentials in the early development of mechanics and thermodynamics, and the emergence of differential calculus and how it was applied to solve some mechanical problems, such as those related to the cycloidal pendulum. The Lagrange equations of motions are presented in th...

We present an analysis of six deterministic models for epidemic spreading. The evolution of the number of individuals of each class is given by ordinary differential equations of the first order in time, which are set up by using the laws of mass action providing the rates of the several processes that define each model. The epidemic spreading is c...

We propose a Langevin equation to describe the quantum Brownian motion of bounded particles based on a distinctive formulation concerning both the fluctuation and dissipation forces. The fluctuation force is similar to that employed in the classical case. It is a white noise with a variance proportional to the temperature. The dissipation force is...

We study the properties of nonequilibrium systems modelled as spin models without defined Hamiltonian as the majority voter model. This model has transition probabilities that do not satisfy the condition of detailed balance. The lack of detailed balance leads to entropy production phenomena which is a hallmark of the irreversibility. By considerin...

Using stochastic thermodynamics, the properties of interacting linear chains subject to periodic drivings are investigated. The systems are described by Fokker-Planck-Kramers equation and exact (explicit) solutions are obtained for periodic drivings as functions of the modulation frequency and strength constants. The limit of long chains is analyze...

Nonequilibrium phase transitions can be typified in a similar way to equilibrium systems, for instance, by the use of the order parameter. However, this characterization hides the irreversible character of the dynamics as well as its influence on the phase transition properties. Entropy production has been revealed to be an important concept for fi...

We use the Landau theory of phase transitions to describe the phase diagram of a liquid crystal displaying the isotropic (i), nematic (N), smectic-A and smectic-C phases. The order parameter of the smectic-C phase is defined as the projection of the director on the plane of the smectic layers, vanishing in the smectic-A phase. We present a detailed...

The Boltzmann kinetic equation is obtained from an integrodifferential master equation that describes a stochastic dynamics in phase space of an isolated thermodynamic system. The stochastic evolution yields a generation of entropy, leading to an increase of Gibbs entropy, in contrast to a Hamiltonian dynamics, described by the Liouville equation,...

Using stochastic thermodynamics, we determine the entropy production and the dynamic heat capacity of systems subject to a sinusoidally time-dependent temperature, in which case the systems are permanently out of thermodynamic equilibrium, inducing a continuous generation of entropy. The systems evolve in time according to a Fokker-Planck or a Fokk...

Non-equilibrium systems under temperature modulation are investigated in the light of the stochastic thermodynamics. We show that, for small amplitudes of the temperature oscillations, the heat flux behaves sinusoidally with time, a result that allows the definition of the complex heat capacity. The real part of the complex heat capacity is the dyn...

The Boltzmann kinetic equation is obtained from an integro-differential master equation that describes a stochastic dynamics in phase space of an isolated thermodynamic system. The stochastic evolution yields a generation of entropy, leading to an increase of Gibbs entropy, in contrast to a Hamiltonian dynamics, described by the Liouville equation,...

Using the stochastic thermodynamics, we determine the entropy production and the dynamic heat capacity of systems subject to a sinusoidally time dependent temperature, in which case the systems are permanently out of thermodynamic equilibrium inducing a continuous generation of entropy. The systems evolve in time according to a Fokker-Planck or to...

The equipartition of energy in its simplest form, which is related to the translational motion of the molecules of a gas, was announced independently by Waterston in 1845 and by Clausius in 1857. In its more general form, it was formulated by Maxwell in 1860. Together with the relation between pressure and translational motion, given by the kinetic...

Nonequilibrium phase transitions can be typified in a similar way to equilibrium systems, for instance, by the use of the order parameter. However, this characterization hides the irreversible character of the dynamics as well as its influence on the phase transition properties. Entropy production has revealed to be an important concept for filling...

According to Sommerfeld, the well known Clausius and Kelvin statements of the second law of thermodynamics comprises two parts. The first part includes the Carnot principle that all Carnot engines operating between the same temperatures have the same efficiency. The second part contains the law of increase in entropy. Usually, the two parts are und...

We investigate the nonequilibrium stationary states of systems consisting of chemical reactions among molecules of several chemical species. To this end, we introduce and develop a stochastic formulation of nonequilibrium thermodynamics of chemical reaction systems based on a master equation defined on the space of microscopic chemical states and o...

We investigate the nonequilibrium stationary states of systems consisting of chemical reactions among molecules of several chemical species. To this end we introduce and develop a stochastic formulation of nonequilibrium thermodynamics of chemical reaction systems based on a master equation defined on the space of microscopic chemical states, and o...

The elementary concepts and fundamental laws concerning the science of heat are examined from the point of view of its development with special attention to its theoretical structure. The development is divided into four periods, each one characterized by the concept that was attributed to heat. The transition from one to the next period was marked...

We study the orientational profile of a semi-infinite system of cylinders bounded in two different ways: by a flat and by a curved wall. The latter corresponds to the interior of a spherical shell, where the dimensions of the rods are comparable to the radius of curvature of the container: they have to accomodate to fill the available space, leadin...

The transport properties of a bosonic chain have been calculated by placing the ends of the chain in contact with thermal and particle reservoirs at different temperatures and chemical potentials. The contact with the reservoirs is described by the use of a quantum Fokker-Planck-Kramers equation, which is a canonical quantization of the classical F...

We analyze a microscopic model for heat transport consisting of two interacting harmonic chains in contact with reservoirs at different temperatures. The chains are mechanically uncoupled but exchange energy randomly through a stochastic noise that affects nearest neighbor particles belonging to distinct chains. We show numerically that the deviati...

We have determined the thermal conductance of a system consisting of a two-level atom coupled to two quantum harmonic oscillators in contact with heat reservoirs at distinct temperatures. The calculation of the heat flux as well as the atomic population and the rate of entropy production are obtained by the use of a quantum Fokker-Planck-Kramers eq...

We have studied the critical properties of the contact process on a square lattice with quenched site dilution by Monte Carlo simulations. This was achieved by generating in advance the percolating cluster, through the use of an appropriate epidemic model, and then by the simulation of the contact process on the top of the percolating cluster. The...

We study the heat transport properties of a chain of coupled quantum harmonic oscillators in contact at its ends with two heat reservoirs at distinct temperatures. Our approach is based on the use of an evolution equation for the density operator which is a canonical quantization of the classical Fokker-Planck-Kramers equation. We set up the evolut...

We have determined the thermal conductance of a system consisting of a two-level atom coupled to two quantum harmonic oscillators in contact with heat reservoirs at distinct temperatures. The calculation of the heat flux as well as the atomic population and the rate of entropy production are obtained by the use of a quantum Fokker-Planck-Kramers eq...

This textbook provides an exposition of equilibrium thermodynamics and its applications to several areas of physics with particular attention to phase transitions and critical phenomena. The applications include several areas of condensed matter physics and include also a chapter on thermochemistry. Phase transitions and critical phenomena are trea...

We analyze a stochastic lattice model describing the spreading of a disease among a community composed by susceptible, infected and removed individuals. A susceptible individual becomes infected catalytically. An infected individual may, spontaneously, either become recovered, that is, acquire a permanent immunization, or become again susceptible....

We study a space structured stochastic model for vertical and horizontal transmitted infection. By means of simple and pair mean-field approximation as well as Monte Carlo simulations, we construct the phase diagram, which displays four states: healthy (H), infected (I), extinct (E), and coexistent (C). In state H only healthy hosts are present, wh...

We study a quantum XX chain coupled to two heat reservoirs that act on multiple-sites and are kept at different temperatures and chemical potentials. The baths are described by Lindblad dissipators which are constructed by direct coupling to the fermionic normal modes of the chain. Using a perturbative method, we are able to find analytical formula...

We study a quantum XX chain coupled to two heat reservoirs that act on multiple-sites and are kept at different temperatures and chemical potentials. The baths are described by Lindblad dissipators which are constructed by direct coupling to the fermionic normal modes of the chain. Using a perturbative method, we are able to find analytical formula...

We use a canonical quantization procedure to set up a quantum Fokker-Planck-Kramers equation that accounts for quantum dissipation in a thermal environment. The dissipation term is chosen to ensure that the thermodynamic equilibrium is described by the Gibbs state. An expression for the quantum entropy production is also provided which properly des...

We use a lattice gas model to describe the phase transitions in nematic liquid crystals. The phase diagram displays, in addition to the isotropic phase, the two uniaxial nematics, the rod-like and discotic nematics, and the biaxial nematic. Each site of the lattice has a constituent unit that takes only six orientations and is understood as being a...

We use the Landau theory of phase transitions to obtain the global phase diagram concerning the uniaxial nematic, biaxial nematic, uniaxial smectic-A and biaxial smectic-A phases. The transition between the biaxial nematic and biaxial smectic is continuous as well as the transition between the nematic phases and the transition between the smectic p...

We describe an approach to model genetic regulatory networks at the level of promotion-inhibition circuitry through a class of stochastic spin models that includes spatial and temporal density fluctuations in a natural way. The formalism can be viewed as an agent-based model formalism with agent behaviour ruled by a classical spin-like pseudo-Hamil...

Systems in which the heat flux depends on the direction of the flow are said to present thermal rectification. This effect has attracted much theoretical and experimental interest in recent years. However, in most theoretical models the effect is found to vanish in the thermodynamic limit, in disagreement with experiment. The purpose of this paper...

Systems in which the heat flux depends on the direction of the flow are said to present thermal rectification. This effect has attracted much theoretical and experimental interest in recent years. However, in most theoretical models the effect is found to vanish in the thermodynamic limit, in disagreement with experiment. The purpose of this paper...

We analyse a non-equilibrium exclusion process in which particles are created and annihilated in pairs and hop to the the right or to the left with different transition rates, $p$ and $q$, respectively. We have studied the dynamics of a single particle, and exactly determined the entropy, entropy production rate and entropy flux as functions of tim...

The critical properties of the stochastic susceptible-exposed-infected model on a square lattice is studied by numerical simulations and by the use of scaling relations. In the presence of an infected individual, a susceptible becomes either infected or exposed. Once infected or exposed, the individual remains forever in this state. The stationary...

We develop the stochastic approach to thermodynamics based on the stochastic dynamics, which can be discrete (master equation) continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of entropy itself and the second, the definition of entropy production rate which is nonnegative and vanishes in th...

We analyze nonequilibrium lattice models with up-down symmetry and two absorbing states by mean-field approximations and numerical simulations in two and three dimensions. The phase diagram displays three phases: paramagnetic, ferromagnetic and absorbing. The transition line between the first two phases belongs to the Ising universality class and b...

Thermal rectification is the phenomenon by which the flux of heat depends on the direction of the flow. It has attracted much interest in recent years due to the possibility of devising thermal diodes. In this paper, we consider the rectification phenomenon in the quantum XXZ chain subject to an inhomogeneous field. The chain is driven out of equil...

We study the entropy production rate in systems described by linear Langevin equations, containing mixed even and odd variables under time reversal. Exact formulas are derived for several important quantities in terms only of the means and covariances of the random variables in question. These include the total rate of change of the entropy, the en...

We analyze the transport of heat along a chain of particles interacting through anharmonic po- tentials consisting of quartic terms in addition to harmonic quadratic terms and subject to heat reservoirs at its ends. Each particle is also subject to an impulsive shot noise with exponentially distributed waiting times whose effect is to change the si...

It has been proposed [Ginelli et al., Phys. Rev. E 71, 026121 (2005)] that, unlike the short-range contact process, the long-range counterpart may lead to the existence of a discontinuous phase transition in one dimension. Aiming to explore such a link, here we investigate thoroughly a family of long-range contact processes. They are introduced thr...

We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, such as dengue, and the threshold of the disease. The coexistence space is composed of two structures representing the human and mosquito populations. The human population follows a susceptible-infected-recovered (SIR) type dynamics and the mos...

Two versions of the threshold contact process–ordinary and conservative–are studied on a square lattice. In the first, particles are created on active sites, those having at least two nearest neighbor sites occupied, and are annihilated spontaneously. In the conservative version, a particle jumps from its site to an active site. Mean-field analysis...

We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, like dengue, and the threshold of the disease. The coexistence space is composed by two structures representing the human and mosquito populations. The human population follows a susceptible-infected-recovered (SIR) type dynamics and the mosqui...

Exact results on particle-densities as well as correlators in two models of immobile particles, containing either a single species or else two distinct species, are derived. The models evolve following a descent dynamics through pair-annihilation where each particle interacts at most once throughout its entire history. The resulting large number of...

We have studied an Ising spin system in a transverse field, at zero temperature, under a time oscillating longitudinal field by means of a mean-field approximation and a Monte Carlo algorithm, appropriate to study the ground-state properties of quantum spin chains. For large values of the transverse field Γ or large amplitude h0 of the oscillating...

The integral equation for computing the density of states of a disordered linear chain of harmonic oscillators is interpreted as describing a stochastic Markov process, and its solution is determined by means of Monte Carlo simulation of the process. It is also shown that, in addition to the localization lengths of the eigenstates, the method allow...

We present a stochastic approach to nonequilibrium thermodynamics based on the expression of the entropy production rate advanced by Schnakenberg for systems described by a master equation. From the microscopic Schnakenberg expression we get the macroscopic bilinear form for the entropy production rate in terms of fluxes and forces. This is perform...

The nonequilibrium stationary state of an irreversible spherical model is investigated on hypercubic lattices. The model is defined by Langevin equations similar to the reversible case, but with asymmetric transition rates. In spite of being irreversible, we have succeeded in finding an explicit form for the stationary probability distribution, whi...

We analyze irreversible interacting spin models evolving according to a master equation with spin flip transition rates that do not obey detailed balance but obey global balance with a Boltzmann–Gibbs probability distribution. Spin flip transition rates with up–down symmetry are obtained for a linear chain, a square lattice, and a cubic lattice wit...

We analyze a threshold contact process on a square lattice in which particles are created on empty sites with at least two neighboring particles and are annihilated spontaneously. We show by means of Monte Carlo simulations that the process undergoes a discontinuous phase transition at a definite value of the annihilation parameter, in accordance w...